The figure is not drawn to scale. LPRV is a parallelogram. NSU and MQT are triangles. ∠NST = 81° and TMQ = 53°. Find
- ∠MNS
- the sum of ∠MTQ, ∠NJQ and ∠QKS.
(a)
∠MNS
= 180° - 81°
= 99° (Interior angles, LP//VR)
(b)
∠NJQ = ∠MJK (Vertically opposite angles)
∠QKS = ∠TKJ (Vertically opposite angles)
MTKJ is a quadrilateral.
∠MTQ + ∠TKJ + ∠MJK + 53° = 360° (Sum of angles in a quadrilateral)
∠MTQ + ∠TKJ + ∠MJK
= 360° - 53°
= 307°
Answer(s): (a) 99°; (b) 307°